Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 95

Table 1.13 Intuitionistic
fuzzy decision matrix B

G 1 G 2 G 3 G 4

y 1 ( 0 . 60 , 0 . 18 )( 0 . 24 , 0 . 44 )( 0 . 10 , 0 . 54 )( 0 . 45 , 0 . 23 )

y 2 ( 0 . 41 , 0 . 25 )( 0 . 49 , 0 . 09 )( 0 . 10 , 0 . 39 )( 0 . 52 , 0 . 45 )

y 3 ( 0 . 62 , 0 . 18 )( 0 . 67 , 0 . 28 )( 0 . 36 , 0 . 42 )( 0 . 12 , 0 . 67 )

y 4 ( 0 . 21 , 0 . 58 )( 0 . 76 , 0 . 22 )( 0 . 48 , 0 . 34 )( 0 . 15 , 0 . 53 )

y 5 ( 0 . 38 , 0 . 19 )( 0 . 65 , 0 . 32 )( 0 . 06 , 0 . 29 )( 0 . 24 , 0 . 39 )

y 6 ( 0 . 56 , 0 . 12 )( 0 . 50 , 0 . 41 )( 0 . 21 , 0 . 07 )( 0 . 06 , 0 . 28 )

functions of the buyer and the supplier). The set of evaluative criteria is denoted by
G

T .
There are six suppliers available, and the set of all alternatives is denoted by
Y

={

G 1 , G 2 , G 3 , G 4 }

= ( . , . , . , . )

, whose weight vector is w 0 34 0 23 0 22 0 21

in
terms of the criteria in G are expressed by the intuitionistic fuzzy decision matrix B
(see Table 1.13 ) (Xia et al. 2012c).

={ y 1 , y 2 ,..., y 6 } . The characteristics of the suppliers y i ( i = 1 , 2 ,..., 6 )

To obtain the alternative(s), the following steps are given (Xia et al. 2012c):
Step 1 Considering all the criteria G j ( j = 1 , 2 , 3 , 4 ) are the benefit criteria, the

performance values of the alternatives y i ( i = 1 , 2 ,..., 6 ) do not need normaliza-

tion.
Step 2 Aggregate the intuitionistic fuzzy values b i of the alternative y i by the
HIFWA operator (without loss of generality, let

γ = 1 ) :

b 1 = (

. , . ),

b 2 = (

. , . ),

b 3 = (

. , . )

0 4075 0 2964 0 4005 0 2466 0 5079 0 3163

b 4 = ( 0 . 4437 , 0 . 4049 ), b 5 = ( 0 . 3783 , 0 . 2734 ), b 2 = ( 0 . 3955 , 0 . 1689 )

Step 3 Calculate the scores S ( b i ) of b i by using Xu and Yager (2006)'s ranking

method:

S ( b 1 ) = 0 . 1111 , S ( b i ) = 0 . 1539 , S ( b 3 ) = 0 . 1915

S ( b 4 ) = 0 . 0388 , S ( b 5 ) = 0 . 1049 , S ( b 6 ) = 0 . 2266

Since

S ( b 6 )> S ( b 3 )> S ( b 2 )> S ( b 1 )> S ( b 5 )> S ( b 4 )

then we can obtain the priority of the alternatives y i ( i = 1 , 2 ,..., 6 ) :

y 6 y 3 y 2 y 1 y 5 y 4

To investigate the variation trends of the scores and the rankings of the alternatives
with the change of the values of the parameter

γ , we use the figures to illustrate these

issues (Xia et al. 2012c).
Figure 1.12 gives the scores of the alternatives obtained by the HIFWA operator as

γ is assigned different values, we can find that the scores for the alternatives decrease

as the values of the parameter

γ

increase from 0 to 10. Figure 1.13 shows the scores